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Position of first occurrence of n in the continued fraction for the Euler-Mascheroni constant (gamma).
2

%I #11 Nov 06 2024 11:53:17

%S 1,3,8,7,10,68,23,13,138,51,21,160,9,198,336,78,162,175,383,613,182,

%T 650,136,479,249,861,553,617,286,299,1951,165,149,2037,559,482,1283,

%U 680,305,19,348,1129,2279,1883,1902,2563,4752,716,30,2609,567,247,2170,7776

%N Position of first occurrence of n in the continued fraction for the Euler-Mascheroni constant (gamma).

%C This sequence is the same as A033149, but uses correct [a_0; a_1, a_2, ...] indexing of continued fraction terms.

%C The smallest numbers not occurring in the first 4,851,382,841 terms of the c.f. are 27943, 33436, 33978, 34017, ... - _Eric W. Weisstein_, Jul 22 2013

%H Eric W. Weisstein, <a href="/A224847/b224847.txt">Table of n, a(n) for n = 1..27942</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Euler-MascheroniConstantContinuedFraction.html">Euler-Mascheroni Constant Continued Fraction</a>

%e The c.f. for gamma is A002852 = [0; 1, 1, 2, 1, 2, 1, 4, 3, 13, ...].

%e 1 occurs first at term a_1

%e 2 occurs first at term a_3.

%e 3 occurs first at term a_8.

%e 4 occurs first at term a_7.

%t With[{cfeg=Rest[ContinuedFraction[EulerGamma,8000]]},Table[Position[cfeg,n,1,1],{n,60}]]//Flatten (* _Harvey P. Dale_, Nov 06 2024 *)

%Y Cf. A033149(n) = a(n) + 1.

%Y Cf. A002852 (continued fraction for Euler-Mascheroni constant).

%K nonn

%O 1,2

%A _Eric W. Weisstein_, Jul 22 2013